KCET · Physics · Thermal Properties of Matter
The amount of heat energy radiated by a metal at temperature \(\mathrm{T}\) is \(\mathrm{E}\). When the temperature is increased to 3T, energy radiated is
- A \(81 \mathrm{E}\)
- B 9E
- C \(3 \mathrm{E}\)
- D \(27 \mathrm{E}\)
Answer & Solution
Correct Answer
(A) \(81 \mathrm{E}\)
Step-by-step Solution
Detailed explanation
According to Stefan's law
\(E \propto T^{4}\)
\(\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\left(\frac{3 \mathrm{~T}}{\mathrm{~T}}\right)^{4} \text { or } \mathrm{E}^{\prime}=81 \mathrm{E}\)
\(E \propto T^{4}\)
\(\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\left(\frac{3 \mathrm{~T}}{\mathrm{~T}}\right)^{4} \text { or } \mathrm{E}^{\prime}=81 \mathrm{E}\)
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